Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
We had interlocking cubes (all the same size) in $10$ different
colours, up to $1000$ of each colour. We started with one yellow
cube. This was covered all over with a single layer of red
This was then covered with a layer of blue cubes. Then came a
layer of green, followed by black, brown, white, orange, pink and
purple for as long as there were enough cubes of that colour to
cover the layer that came before.
The unused cubes were put away. The many-layered cube was then
broken up and each colour made into cubes. These were just of the
one colour and the largest cubes possible made. For example, the
red layer made three $2\times 2\times2$ cubes with two $1\times
1\times1$ cubes left over, whereas the larger layers made much
larger cubes as well as smaller ones.
What colour was the largest cube that was made?
Which colour made into cubes had no $1\times 1\times1$
Which colour was made into the most cubes including the $1\times